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Pompey never attained the supreme power that Caesar (briefly, before he was murdered, did). Although he at times (such as when he was fighting the pirates or when he was consul sine collegio in the late 50s BCE) had great imperium, he was always either reluctant or unable to arrogate to himself the fount of this power. Therefore, he was always either a member of a power-sharing arrangement or the champion of the conservative/reactionary party. So he can't be really counted as a ruler.

Having said that, I must say that some scholars do espouse the view that you suggested - that Pompey can be viewed as the first princeps. Not being a professional, I don't have a ready reference for that right now, but some googling led me to a corroboration of this statement (p. 240 there):

Pompey the Great, considered by some to be the first princeps, had
unmatched influence in Rome, which conflicted with the Republican
system that restricted such a consolidation of influence (Beard and
Crawford 85).

EDIT: I found it! The great Syme himself penned the memorable suggestion that had Pompey won he would have been killed at the foot of his own statue by honourable men.